Problem statement A MASSOFSKOIS RELEASED FROM A HEIGHT OFSmeterspowN SLOPEOF20 D

Question

Problem statement A MASSOFSKOIS RELEASED FROM A HEIGHT OFSmeterspowN SLOPEOF20 DEGREES DATA THE DIMENSIONS ARE STATED IN THE FIGURE THE SLOPE HAS NO FRICTION THE FRICTION BETWEEN POINTS a AND b is m-0.55 THERE IS NO FRICTION ON THE SURFACE UNDER THE SPRING QUESTIONS 1. What speed the mass of 15 kg has when it reaches point b 2. Does the mass of 15 kg reach point a? 3. If the moss reaches point o, how much is the spring compressed 4. Answer questions 1, 2 and 3 if there is friction on all the surfaces m 15 kg K=750 N/m h1 = 5m 0-20 1m a 7 m

Explanation / Answer

here,

mass , m = 15 kg

height , h = 5 m

1)

the speed of mass at b , u = sqrt(2 * g * h)

u = sqrt(2 * 9.81 * 5) m/s

u = 9.9 m/s

2)

u^2 = 9.9^2 = 98.1 m^2/s^2

(2 * (uk * g) * 7) = (2 * ( 0.55 * 9.81 * 7)) = 75.5 m^2/s^2

as (2 * a * s) > u^2

the block will reach a

v^2 - u^2 = - 2 * a * s

v^2 = 98.1 - 75.5

v = 4.75 m/s

3)

let the spring streches x m

0.5 * K * x^2 = 0.5 * m * v^2

750 * x^2 = 15 * 4.75^2

solving for x

x = 0.67 m

4)

as uk > tan(20)

the block will not move

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